Cristina Odone: "I must stress here that I embrace the concept of religion as faith rather than simply a structure like the Vatican or a synagogue. When I think of religion I think of the injunctions that it has given its followers. Repair the world, a Jewish commandment. Love thy neighbour as thyself, the most famous Christian commandment. And look upon charity as something that you must do every day that the sun rises, which is a Muslim injunction.

"I think without such wonderful exhortations, our spirit would be the poorer and so would our society. And I think it is one of the tenets of religion, of all the major monotheistic religions, that each one of us is special, that each one of us deserves respect, having been made by God. I think that is something at the very heart of a good society."

Jon Cruddas: "I agree. I think the generic element of all religions is the search for compassion. That's quite a good departure point in terms of how you live your life… the search for virtue in our world."

Evan Harris: "I agree with [Cristina] only in the sense that she's appropriated to religion obvious moral rules that apply equally to people without religion. So you can't really defend religion by claiming unto religion rules that predated them, that are statements of the obvious. And the real question is, 'What would the world be like without organised religion'? Everyone has beliefs – it's not reasonable to suggest that people wouldn't have beliefs, mystical or otherwise. I think I'm with John Lennon on this, that it would be a much better place in terms of peace.

"There's a wish to label those people who believe that there should be less of a role for religion in public policy, as somehow extreme, when they're not extreme. I've looked carefully at what's been done in the name of religion..."

CO: "And in the name of secularism, Evan? Fascism, communism?"

EH: "All that I could find in the name of atheism or secularism is a ban on head-scarves in Turkish universities and a proposed burqa ban in France. Both are wrong, but if that's the worst that's done in the name of a lack of religion, I'd rather run those risks. I mean, apostasy, blasphemy… It's bad news for women and gay people where organised religion plays a major role in public policy."

AA: Anthony, you're nodding in agreement. But is there an argument that the good perhaps even in atheist people today is something that is the result of religion's influence?

AC Grayling: "No. If you think about the dominance of Christianity in Europe, which really took hold right about the fourth century AD, that was nearly 1,000 years after Socrates and Plato and Aristotle had begun to think about the nature of the good and the good society. Have a look at the New Testament documents or those that were selected by the church as canonical. They say: give away all your money, turn your back on your family if they don't agree with you. If people do bad things, help them to do them more, turn your other cheek. Take no thought for tomorrow, make no plans.

"This was a morality, an unliveable morality premised on the idea that the world was very shortly to end, it was going to end next week or next month.

"And when after several centuries had passed by and the parousia hadn't happened, they began to import wholesale the wonderful heritage of ethics that had been discussed by the Stoics and the Epicurians and the Aristotelians for centuries before their time.

"What we think of as distinctive of western morality has its roots in the non-religious secular tradition of ethics that comes from classical antiquity."

Samia Rahman: "I see religion and the practice of religion as often an extension of [an] individual's personality and their existing thoughts and beliefs and their characteristics. And so I see this oppositionality between belief and non-belief as almost a moot point. We have shared values. Religion offers many people a framework and a moral compass and they navigate through the framework and through the guidelines that their religion offers them and they come to their own conclusion and their own way of living.

"So I do have difficulty with the dichotomy between belief and non-belief and I think we can look at the intersections and where we do agree and gain something from that, rather than constantly positioning ourselves as the other."

AA: What about the charge that [religion is] also responsible for many very negative things?

CO: "What I think we who believe are very conscious of is that we want to take the best of religion and we don't want to take on the bad bits. We don't want to in any way condone paedophile priests. We don't want to in any way condone the lachrymose televangelist in America who takes up millions and then makes away with the church funds. But what we are saying is that despite the corruption of the ideal, that ideal remains an inspiration for millions the world over."

AG: "I welcome tremendously the concessive and inclusive attitude of people who have a faith and say they want to co-exist with other people who have [no] faith, [who] cherry-pick the best bits of their religion and leave the undesirable bits, the anti-gay, the anti-women, the burn-them-at-the-stake bits. I welcome that. And that is a function of our secularism, in fact. The fact that since the Enlightenment, the churches, which when they were in power were able to exercise tyrannical control over people's lives and thoughts and beings, they've been pushed back into a corner. It's really interesting that wherever religion is on the front foot, it bears down in a very impressive [way] on people. Look at the Taliban.

"Wherever they're on the back foot, they suddenly become very friendly, very concessive and very tolerant. And that's where they should be, very firmly on the back foot."

CO: "I think that what we have seen in the past may have been the oppression by some church institutions of people who were not believers. What we're seeing in the present is the oppression, the hunting down of believers, whether it is the Muslim community who feel every day that they open the newspaper, 'Oh my gosh, it's anti-Islam again', or the Christian BA worker who is not allowed to wear a cross, or the school play that is not allowed to be called the nativity play."

EH: "Clearly some religious minorities are oppressed. But I don't think we can accept, and I don't think one should accept, the idea of Christian victimhood in this country. Because there are huge privileges accorded to religion and particularly Christianity in this country... There are charitable dispensations for religion. Religions are allowed, uniquely, the exemption to discriminate against people on the grounds of sexual orientation in a way that gay people are not allowed. It's only religious schools that can discriminate against the non-religious or the other-religious. So I don't think we should accept for a moment this religious victimhood.

"But a liberal, secular democracy is the best protector of religious freedom, because it says that we need to guarantee the absolute freedom of belief. There is no theocracy that has ever provided for religious freedom, let alone emancipation of women and equal rights for gay people."

AG: "I second all that. There's an important additional point of view, that religious organisations should recognise themselves for what they truly are, which is self-constituted interest groups. They're civil society organisations which exist to put a point of view. They have every right to have their say, but in our society they have a massively over-amplified voice, massively oversized footprint in the public square, and that's wrong. They're like trade unions or political parties and the rest of them. Let them have their say, but don't give them this artificial amplification of seats in the House of Lords, and four hours of broadcasting on the BBC every day, and faith-based schools and the rest of it, because it distorts our society."

JC: "I come at this from a slightly different approach. [Faith] is one of the forces which resists the commodification of our lives, and that is the struggle. It seems to be self-evident in terms of the destructive way that capitalism has deracinated our culture and our lives: [there are] redeeming elements in the world that can safeguard and fight against that commodification in our lives, and faith communities are one of them."

CO: "That is absolutely right, and I think that is one of the elements of religion that anti-religious commentators never want to focus on. It is so subversive because it questions – it challenges the materialism, the consumerism, the individualism that is wrecking our society."

AG: "Any organisation that wants you to sign up for its version of the One Big Truth, tells you how to live your life, how to behave, what you should believe, what you're not allowed to believe, how you should comport your life... traditionally religion is in the business of doing that the whole time."

SR: "That's not confined to religion. You look at China, you look at various states around the world who are secular societies."

AG: "You're quite right about that, but they all have one thing in common, which is: we know the answer, you've got to fall in line, and if you don't you're in trouble. You might be as against the People's Republic of China government as you might be against the Church, or against Islam. They all want to own your attitudes and actions."

SR: "But that does not negate religion as a force for good. That does not negate the fact that religion does call into question individualism, and this idea of rampant consumerism. Religion offers an alternative to that."

EH: "But there's a flip side of that – because religions are sometimes, and we must be careful not to generalise, hostile to a human rights approach, because that implies that there are individual and alienable human rights that are not consequent on God-given entities. But I do want to focus on what justifies a faith school, state-funded, discriminating against a teacher on the basis of their sexual orientation or their religion.

"I think what society desperately needs is for young people, particularly in school, to mix as much as possible with people of other races and religions. And discrimination in schools for pupils tends to add to existing segregation based on housing in this country, and so I think there's a public policy imperative to prevent that segregation and discrimination."

JC: "My problem is I just don't recognise this world. Every single one of my very large extended family is a product of Catholic comprehensive education. I think it's a force for good in this country, I think it creates wiser, more rounded young people – students who learn about different alternative belief systems and they resist certain other forces in our societies."

AA: Are you saying that those other forces are all non-religious forces?

JC: "No, I didn't say that at all. It seems to me that this debate can be dominated by caricature. I just think we should have a plurality of different schools."

EH: "If you have an area with four schools, three of which are church schools, which often happens, a non-religious or wrong-religious family has the choice of one. The religious person has the choice of all four. That is not fair, and it isn't justified."

CO: "What everyone overlooks is our right as a minority to teach our children the ethics that we were taught."

EH: "No-one's stopping you… Religious education should be about what religions believe, not telling children what to believe – that's the role of the family and the Church."

CO: "Religious education allows children to be brought up with an understanding of a spiritual framework, and it's not just their spiritual framework. I have a daughter in a Catholic state school, and what I have been so impressed by is how her teacher, who's an Anglican, has said: I want you to explore the synagogue and listen to what they're teaching there, I want you to explore the mosque and listen to what they're teaching there, and then yes, we come back and we talk about the differences between the religious systems, but the most important thing is we learn respect for other religions."

AG: "Neither Cristina nor Jon, with respect, are really picking up the challenge that Evan is giving them here. Why don't you do all this religious education and encouragement in the family setting and in your church? Why are you, as Evan put it, co-opting the state to help do it for you? That's point number one. Point number two is this: I visited a faith-based school and they started by saying, 'At this school we promote mutual understanding, and tolerance, and conviviality,' and they were very proud of themselves for doing it. And I said, that is not something that we should praise you for – that is something we should expect from you as a minimum...

"It happened to be a Church of England school, but it had Muslims in it, and Catholics. And I asked each of these girls, who were all friends – I said to the Muslim girl, 'What's going to happen to your Catholic friend here when she dies?' And I [said] to the Catholic girl, 'What's going to happen to your Muslim friend here when she dies?' And so on. Oh, gasps went up from the teachers and the bishop to say you're being divisive and you're asking an unpleasant question, and I said, 'No I'm not – I'm trying to get them to think through to the consequences of what they're really committed to believing.'"

CO: "Anthony – you must stick to philosophy, do not venture into unknown territory. The Catholic teaching is not about ours being the only way."

SR: "I think when you enter into such theological arguments, what you have to remember – particularly it's true of Islam and the Qur'an – [is] there is a high level of interpretation of the text, and contextualisation. And I think that's something that really needs to be borne in mind when you talk about the way that women are treated in religion, the way that non-believers are treated. There are various strands of thought... so it's rather unfair to dismiss religion as being anti-women, homophobic."

AA: Samia, is it unfair for others to question how people within religion deal with those sorts of issues?

SR: "No, that's not unfair at all. That's something that we, as a faith, are constantly doing – reinterpreting the texts."

EH: "I don't know any Muslim woman priests, I don't know any Catholic women priests, or actively gay priests in those areas. So the evidence [is] that organised religion – I'm sure there are dissenters – is not good news for women and gay people, even in their own church.

"But when it comes to public policy they argue for discrimination, and I think that's a problem. And religions say, 'Oh, women are too good for this – we place them on a pedestal.' Religions tend to place women beneath a pedestal, in the words of Woody Allen, and it's very hard to identify any religious state, or heavily religiously influenced state, that doesn't have real difficulties for women and gay people."

JC: "Look, the notion that you have a very prescriptive belief system that you singularly attach yourself to, if you are part of one denomination or another, is a total falsehood. These are complex issues – they ricochet through all of these religions. It's the absolutism, it's the intolerance that dominates this new atheism, which I will react against, actually, because it's so illiberal, and it's so metropolitan as well…"

EH: "I want to touch back on that, if I may, because you're able to say what you just said – there can be these debates, and disagreements, and flexibilities within faiths and between faiths about these matters – only because you now live in a functionally secular society. Had you lived 300 or 400 years ago, you wouldn't be."

JC: "When I listen to Dawkins or Sam Harris, or Hitchens, it's the absolutism, it's the intolerance. They sound like religious fundamentalists – there's no respect, no tolerance, no fluidity."

SR: "Religion is often a leap of faith for many people, but so is atheism. I see atheism in a similar way – that it is a leap of faith, because we're talking about the unknowable."

AA: Can I ask a question on that point? Perhaps to Evan. It's interfaith week this week, and one thing that I think is interesting is that religion... fulfils a very human need. If there were no religion, what would exist instead to fulfil that need?

EH: "The agenda that I have, which is to see a secular society, involves people having absolute freedom to believe, but not impose it on others, and maximum freedom of discourse to have this discussion. So I think the real question, the public policy question, is: do we believe that we should separate the Church and religion? Should we end religious privilege, and try to maximise individual freedom of religious belief and the ability of religious organisations to organise themselves so that they do not discriminate against or limit the freedoms of other people outside of that religious organisation?

"Why do we have a constitution that says to William and Kate, if they have children, that if it's a girl that girl will have to wait behind other male children, and if William had married a Catholic he would have to leave the succession? That is wrong and our religious state doesn't want to change that."

JC: "We haven't talked about the deeper questions that we're trying to raise. What is our culture, what are we seeking to resist in terms of the relentless destruction of it? I joined the Labour party because it was built around a notion of duty, obligation, service, commonality in terms of the search for a better world."

AA: I would like to discuss all of those issues more but before we do that, you are a Labour politician and you do have to answer questions surely about whether religion's influence oversteps the mark within…

JC: "I do. I don't accept all of the creeds of our leaders in our Church, to tell you the truth, because I am a rebel in these things but I just refuse to accept this caricature that is dominant in terms of these debates. I just think, let's focus on nuance."

AA: Jon, do you believe that lots of the good things that you see Catholicism perhaps giving to you through your life would have existed without religion?

JC: "No I don't. I think that it was basically through the diaspora and the role of religion, in terms of cohering and retaining a certain belief system. That was absolutely critical in terms of the whole genealogy of my family."

CO: "Anushka's question was, what would we have instead of religion in order to have a good society [and] I think communitarianism which is what Jon was talking about. And Cameron has his big society. I really believe he's struck a nerve and I think that what is so important is that when you start examining these two concepts, these two competing concepts, what do we find? That they're all incredibly similar to the religious framework: it is about charity; it is about loving others; it is about respect, it is about volunteering. It's about not being materialistic."

AG: "Don't keep hijacking these notions as if [they are] monopolised by religion. You and I, Jon, will probably agree on very, very many points, politically and socially. I have exactly the same attitude to the need for society to be richly and deeply moral. In fact humanism, which is the idea that we premise our understanding of ethics on our best, most generous and sympathetic understanding of human nature and the complexities of the human condition, is a very ancient tradition which pre-dates all the major religions in the world today and which they have adopted.

"What one wants to do is to concentrate on those commonalities, get rid of the doctrinal differences and divisions."

AA: Anthony, you wrote recently that you believe that the influence of religion is negative. Can you just explain how you came to that conclusion?

AG: "I accept that religious faith on the individual level can be something that sustains and succours people as can a deep commitment to the communist cause, the psychological prop of identifying yourself with something is a well-established fact. But when you look at history what you see overwhelmingly is division, you see conflict, you see the oppression of the individual. And I think on balance it's been a very bad thing that religious organisations have had such power over human individuals and societies for centuries."

SR: "What I find difficult is often the discourse of religion versus secularism and 'is religion a force for good?' becomes wrapped up in this idea of demonising the other. I think, as a Muslim, we do feel this rather keenly. Not wishing to enter into this sense of victimisation but there is quite a marked Islamophobia which exists, not just in the UK but across Europe."

EH: "I'm not sure from my study of it that Islamophobia is founded on objections to the Muslim's belief in one God, or indeed in the Prophet. I think much of Islamophobia is racism dressed up as anti-religion and I think Muslims are victims of that – I'm with you 100% – but I don't think it's because of an anti-religious feeling."

JC: "What interests me is the future debates, the coming cultural wars, the framing that you see. Mosque in Manhattan, how that's linked to certain evangelical movements in this country, linked into the English Defence League, linked into a virulent form of Islamophobia and unless there are more radical religious elements in this mix I think you're going to see the terms of debate radically move and be caricatured between a religious debate and a metropolitan, liberal debate and there is no space in the middle. And we have to occupy those spaces."

AG: "Is part of the solution more Muslim schools for Muslims?"

EH: "Northern Ireland surely teaches us – I know it's complex and it's not just this – but if you educate children in a segregated way then it's much more difficult for people to be seen as something other than the other. I think segregation of children is deeply invidious to a cohesive society."

CO: "What you call segregation some people call community and what us Catholics felt during the IRA days here in England was really hunted and haunted in the way that the Muslim community feels now. And one way of shoring up our defences was to attend schools where we didn't feel that we were the victims, where we didn't feel that we were the suspected terrorist at every step of the way. And what you call invidious ghettos were great defences, they were havens, oases of peace and respect."

AG: "You describe that as a solution to a difficulty that [the] community in question faced, but in fact it's a consequence of the ghettoisation that had already occurred beforehand. Had there been no such divisions there would have been no driver for people pulling up the drawbridges around those ghettos.

"When I think about four-, five- and six-year-old kids in kindergartens and primary school, they don't know that they're Catholic, Muslim, Protestant or anything else. They're just children. They get on with one another, they don't care about skin colour or creed or ethnicity or even language. My little daughter went to a school where there were 36 different languages spoken, an absolute rainbow place, it was wonderful. It takes a lot of energy and effort to teach those kids that they're different from others... that other people are not the same as them, perhaps not as good as them. And that's a tragedy."

AA: We haven't touched on the religious right in America.

JC: "That's a thing that worries me... Unless there is a more radical religious contribution that can drown out or crowd out the religious right and the way they are systematically framing cultural debates across mainland Europe… It's interlinked with the crisis of social democracy as well, where social democracy is almost the haven for a liberal metropolitan elite and bits of the public sector.

"The religious right is systematically redefining the terms of public debate around flag, nationhood, religion and family and unless that is the real contested terrain then I think we are in real trouble, culturally across western market economics."

AA: I want to come back to the question that we're asking: is religion a force for good in the world?

CO: "I think, absolutely, yes – it is a force for good in the world and the challenge for our society is to take the good that religion offers and excise the bad."

EH: "The key question is not whether religion is a force for good in the world. For policymakers it is: to what extent can we change things in respect of religion? What we should seek to do is take organised religion out of the state and out of politics in terms of privilege so that there is a level playing field for all religions and none."

SR: "I think religion and the practice of religion is a complex journey for many people and I think that needs to be recognised. You have a minority of extremist Christians or extremist Muslims and the overwhelming majority of peaceful believers do not share that point of view. The moderate view is drowned out."

AG: "I think that a good world would be one in which people approached one another first and foremost as fellow human beings with whom they share far more than they have differences. Thinking of the people you encounter in the world as fellow human beings means that you put that fact before their gender, their sex or sexuality or their political orientation or their religious views or their social background or how much money they've got. And if we were to think in those terms, and I think of that as a fundamentally humanist approach to the world, it would be much more of a global community."

JC: "I agree with an awful lot of that actually. You see there is, once you reach beyond caricature, once you reach beyond the absolutism within which this new atheism is framed, there's a lot that can be respected across this whole divide."

• This article was amended on Monday 22 November 2010 and Friday 26 November 2010. 'EH' and 'AG' were confused on four occasions; this has been corrected. 'People' was changed to 'male children'.